(3x^2+2)/(x^2-4)-(9x-x^2)/(x^2-4)

Your problem:

(3x^2+2)/(x^2-4)-(9x-x^2)/(x^2-4)

Since the denominator is the same, just subtract the numerator:

(3x^2 + 2 - 9x + x^2)/(x^2 - 4) -->remember to use the distributive property with the negative over the terms in the numerator of the second fraction.

Combine like terms:
(4x^2 - 9x + 2)/(x^2 - 4)

Can we factor to reduce this fraction? Yes.

(4x - 1)(x - 2)/(x + 2)(x - 2)

Can you take it from here to reduce this fraction? (Hint: cancel out the same factors in both the numerator and denominator to reduce.)

I hope this will help.

thank you sooo much. now I know what I did wrong. First I got 2x^2 instead of 4x^2 and then I couldn't manage tpfactor because I didn't see were the nine would fit in. Thanks you for the help!

You're welcome! I'm glad I could help you find the mistake and understand the correct steps. Don't worry, making mistakes is all part of the learning process. It's great that you were able to identify your error and learn from it. If you have any more questions or need further assistance, feel free to ask. Good luck with your math!

You're welcome! I'm glad I could help you identify the mistake and understand the process of factoring. It's quite common to make small errors while solving algebraic expressions, so don't worry too much about it. Taking your time and double-checking your work can help catch those mistakes. If you have any more questions or need further assistance, feel free to ask. Keep up the good work!